A certain company's main source of income is a mobile app. The company's annual profit (in millions of dollars) as a function of the app's price (in dollars) is modeled by $P(x)=-2(x-3)(x-11)$ Which app prices will result in $\$0$ annual profit? Enter the lower price first. Lower price:
Answer: The annual profit is $\$0$ when $P(x)=0$. $\begin{aligned} P(x)&=0 \\\\ -2(x-3)(x-11)&=0 \\\\ \swarrow &\searrow \\\\ x-3=0\text{ or }&x-11=0 \\\\ x=3\text{ or }&x=11 \end{aligned}$ In conclusion, these are the app prices that will result in $\$0$ annual profit: Lower price: $3$ dollars Higher price: $11$ dollars